Selecting among three‐mode principal component models of different types and complexities: A numerical convex hull based method

Several three‐mode principal component models can be considered for the modelling of three‐way, three‐mode data, including the Candecomp/Parafac, Tucker3, Tucker2, and Tucker1 models. The following question then may be raised: given a specific data set, which of these models should be selected, and at what complexity (i.e. with how many components)? We address this question by proposing a numerical model selection heuristic based on a convex hull. Simulation results show that this heuristic performs almost perfectly, except for Tucker3 data arrays with at least one small mode and a relatively large amount of error.     

Ignorance or integration: the cognitive processes underlying choice behavior

The fast‐and‐frugal heuristic framework assumes noncompensatory tools for human preferences (i.e., priority heuristic) and inferences (i.e., take the best heuristic). According to this framework, these heuristics predict choice behavior as well as model the cognitive processes underlying such behavior. The current paper presents two studies that juxtapose predictions derived from these two simple heuristics with alternative predictions derived from compensatory principles. Dependent measures that included reaction time, choice pattern, confidence level, and accuracy were better predicted by compensatory indices than by noncompensatory indices. These findings suggest that people do not rely on limited arguments only, but tend to integrate all acquired information into their choice processes. This tendency was replicated even when the experimental task facilitated the use of noncompensatory principles. We argue that the fast and frugal heuristics can predict the final outcome only under certain conditions, but even in these particular situations they are not applicable to the processes underlying choice behavior. An integrative model for choice behavior is proposed that better represents the data. Copyright © 2009 John Wiley & Sons, Ltd.     

Thinking straight while seeing red: the influence of anger on information processing

Because angry people apparently rely on heuristic cues when making judgments, anger has been claimed to trigger superficial, nonanalytic information processing. In three studies, the authors found that induced anger promoted analytic processing. Experiment 1 showed that angry participants were more likely to discriminate between weak and strong arguments than participants in neutral moods. Experiment 2 demonstrated that anger overrode dispositional preferences not to process, causing even those low in need for cognition to process analytically. Experiment 3 reconciled these findings with previous work by showing that angry people used accessible, valid, and relevant heuristics but otherwise processed analytically, as indicated by attitude change and elaboration data. Together, these experiments showed that angry people can have both the capacity and motivation to process and that their selective use of heuristics reflects the cue's perceived validity and not the failure to process analytically.     

A fast method for choosing the numbers of components in Tucker3 analysis

Recently, Timmerman and Kiers proposed an effective procedure for choosing the numbers of components in Tucker3 analysis, a kind of component analysis of three‐way data. The procedure, however, is rather time‐consuming, relying on very many complete Tucker3 analyses. Here, an alternative procedure is proposed, which basically relies on a single, quick analysis of the three‐way data set. In a simulation study it was found that the new procedure is comparable in its effect to the original procedure.     

Coherence shifts in probabilistic inference tasks

The fast‐and‐frugal heuristics approach to probabilistic inference assumes that individuals often employ simple heuristics to integrate cue information that commonly function in a non‐reciprocal fashion. Specifically, the subjective validity of a certain cue remains stable during the application of a heuristic and is not changed by the presence or absence of another cue. The parallel constraint satisfaction (PCS) model, in contrast, predicts that information is processed in a reciprocal fashion. Specifically, it assumes that subjective cue validities interactively affect each other and are modified to coherently support the favored choice. Corresponding to the model's simulation, we predicted the direction and the size of such coherence shifts. Cue validities were measured before, after (Experiment 1), and during judgment (Experiments 2 and 3). Coherence shifts were found in environments involving real‐world cue knowledge (weather forecasts) and in a domain for which the application of fast‐and‐frugal heuristics has been demonstrated (city‐size tasks). The results indicate that subjective cue validities are not fixed parameters, but that they are interactively changed to form coherent representations of the task. Copyright © 2009 John Wiley & Sons, Ltd.     

Tucker3 hierarchical classes analysis

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.The first author is a Research Assistant of the Fund for Scientific Research-Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2000/02). We are grateful to Kristof Vansteelandt for providing us with an interesting data set.     

The similarity heuristic

Decision makers often make snap judgments using fast‐and‐frugal decision rules called cognitive heuristics. Research into cognitive heuristics has been divided into two camps. One camp has emphasized the limitations and biases produced by the heuristics; another has focused on the accuracy of heuristics and their ecological validity. In this paper we investigate a heuristic proposed by the first camp, using the methods of the second. We investigate a subset of the representativeness heuristic we call the “similarity” heuristic, whereby decision makers who use it judge the likelihood that an instance is a member of one category rather than another by the degree to which it is similar to others in that category. We provide a mathematical model of the heuristic and test it experimentally in a trinomial environment. In this environment, the similarity heuristic turns out to be a reliable and accurate choice rule and both choice and response time data suggest it is also how choices are made. We conclude with a theoretical discussion of how our work fits in the broader “fast‐and‐frugal” heuristics program, and of the boundary conditions for the similarity heuristic. Copyright © 2009 John Wiley & Sons, Ltd.     

Chunk hierarchies and retrieval structures: Comments on Saariluoma and Laine

The empirical results of Saariluoma and Laine are discussed and their computer simulations are compared with CHREST, a computational model of perception, memory and learning in chess. Mathematical functions such as power functions and logarithmic functions account for Saariluoma and Laine's correlation heuristic and for CHREST very well. However, these functions fit human data well only with game positions, not with random positions. As CHREST, which learns using spatial proximity, accounts for the human data as well as Saariluoma and Laine's correlation heuristic, their conclusion that frequency-based heuristics match the data better than proximity-based heuristics is questioned. The idea of flat chunk organisation and its relation to retrieval structures is discussed. In the conclusion, emphasis is given to the need for detailed empirical data, including information about chunk structure and types of errors, for discriminating between various learning algorithms.     

The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component Analysis

Parafac2 is the most flexible Simultaneous Component Analysis (SCA) model that produces an essentially unique solution. In this paper, we discuss how Parafac2’s special sign indeterminacy affects applications of SCA, and we reveal how an external criterion variable can be used to ensure that estimated Parafac2 weights are meaningfully signed across the levels of the nesting mode. We present an example with real data from clinical psychology that illustrates the importance of Parafac2’s special sign indeterminacy, as well as the effectiveness of our proposed solution. We also discuss the implications of our results for general applications of SCA.     

The Impact of Inappropriate Modeling of Cross-Classified Data Structures

Cross-classified random effects modeling (CCREM) is used to model multilevel data from nonhierarchical contexts. These models are widely discussed but infrequently used in social science research. Because little research exists assessing when it is necessary to use CCREM, 2 studies were conducted. A real data set with a cross-classified structure was analyzed by comparing parameter estimates when ignoring versus modeling the cross-classified data structure. A follow-up simulation study investigated potential factors affecting the need to use CCREM. Results indicated that when the structure is ignored, fixed-effect estimates were unaffected, but standard error estimates associated with the variables modeled incorrectly were biased. Estimates of the variance components also displayed bias, which was related to several study factors.     

Tucker2 hierarchical classes analysis

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of the Tucker2-HICLAS model, being closely related to the Tucker3-HICLAS model (Ceulemans, Van Mechelen & Leenen, 2003), is that one of the three modes is minimally reduced and, hence, that the differences among the association patterns of the elements of this mode are maximally retained in the model. Moreover, as compared to Tucker3-HICLAS, Tucker2-HICLAS implies three rather than four different types of parameters and as such is simpler to interpret. Two types of Tucker2-HICLAS models are distinguished: a disjunctive and a conjunctive type. An algorithm for fitting the Tucker2-HICLAS model is described and evaluated in a simulation study. The model is illustrated with longitudinal data on interpersonal emotions. The first author is a Researcher of the Fund for Scientific Research—Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2000/02). The authors are grateful to Iwin Leenen for the fruitful discussions.     

Power boosts reliance on preferred processing styles

A significant amount of research has proposed that power leads to heuristic and category based information processing, however, the evidence is often contradictory. We propose the novel idea that power magnifies chronically accessible information processing styles which can contribute to either systematic or heuristic processing. We examine heuristic (vs. systematic) processing in association with the need for closure. The results of three studies and a meta-analysis supported these claims. Power increased heuristic information processing, manifested in the recognition of schema consistent information, in the use of stereotypical information to form impressions and decreased the complexity of categorical representations, but only for those participants who, by default, processed information according to simplified heuristics, i.e., are high in need for closure. For those who prefer this processing style less, i.e., low in need for closure, power led to the opposite effects. These findings suggest that power licenses individuals to rely on their dominant information processing strategies, and that power increases interpersonal variability.     

科学发明中原型启发的创造性思维成分及其脑机制

目前对创造性思维的测量及神经机制的研究, 国际上大多采用发散思维任务、远距离联想测验、顿悟问题解决等任务。但这些测量工具大多停留在对非科学类问题解决的研究上, 因此生态效度和预测效度都不高。本项目在前面研究的基础上, 探讨更符合现实生活的科学发明中原型启发的创造性思维成分及机制。研究一通过两个行为实验探索原型启发能力的创造性思维成分测试的结构效度; 研究二运用大样本磁共振数据, 从脑机制上进一步验证创造性思维成分的结构效度; 研究三通过3个核磁任务态探索原型启发能力的主要创造性思维成分的脑机制; 研究四试图在高校和企业研发机构进行跟踪研究, 检验创造性思维成分测试的预测效度。通过本项目的开展, 希望开发具有更高预测效度和生态效度的用于发明创造领域的创造性测量工具。     

SIMPLIFYING HEURISTICS VERSUS CAREFUL THINKING: SCIENTIFIC ANALYSIS OF MILLENNIAL SPIRITUAL ISSUES

There is ample evidence that humans (and other primates) possess a knowledge instinct—a biologically driven impulse to make coherent sense of the world at the highest level possible. Yet behavioral decision‐making data suggest a contrary biological drive to minimize cognitive effort by solving problems using simplifying heuristics. Individuals differ, and the same person varies over time, in the strength of the knowledge instinct. Neuroimaging studies suggest which brain regions might mediate the balance between knowledge expansion and heuristic simplification. One region implicated in primary emotional experience is more activated in individuals who use primitive heuristics, whereas two areas of the cortex are more activated in individuals with a strong knowledge drive: one region implicated in detecting risk or conflict and another implicated in generating creative ideas. Knowledge maximization and effort minimization are both evolutionary adaptations, and both are valuable in different contexts. Effort minimization helps us make minor and routine decisions efficiently, whereas knowledge maximization connects us to the beautiful, to the sublime, and to our highest aspirations. We relate the opposition between the knowledge instinct and heuristics to the biblical story of the fall, and argue that the causal scientific worldview is mathematically equivalent to teleological arguments from final causes. Elements of a scientific program are formulated to address unresolved issues.     

Convex hull or crossing avoidance? Solution heuristics in the traveling salesperson problem

Untrained adults appear to have access to cognitive processes that allow them to perform well in the Euclidean version of the traveling salesperson problem (E-TSP). They do so despite the famous computational intractability of the problem, which stems from its combinatorial complexity. A current hypothesis is the humans' good performance is based on following a strategy of connecting boundary points in order (the convex hull hypothesis). Recently, an alternative has been proposed, that performance is governed by a strategy of avoiding crossings. We examined the crossing avoidance hypothesis from the perspectives of its capacity to explain existing data, its theoretical adequacy, and its ability to explain the results of three new experiments. In Experiment 1, effects on the solution quality of number of points versus number of interior points were compared. In Experiment 2, the distributions of observed paths were compared with those predicted from the two hypotheses. In Experiment 3, figural effects were varied to induce crossings. The results of the experiments were more consistent with the convex hull than with the crossing avoidance hypothesis. Despite its simplicity and intuitive appeal, crossing avoidance does not provide a complete alternative to the convex hull hypothesis. Further elucidation of human strategies and heuristics for optimization problems such as the E-TSP will aid our understanding of how cognitive processes have adapted to the demands of combinatorial difficulty.     

Real‐World Correlates of Performance on Heuristics and Biases Tasks in a Community Sample

In the current study, we sought to examine whether performance on several heuristics and biases tasks and thinking dispositions was associated with real‐life correlates in a community sample of adults. We examined performance on five heuristics and biases tasks (ratio bias, belief bias in syllogistic reasoning, cognitive reflection, probabilistic and statistical reasoning, and rational temporal discounting), three thinking dispositions (actively open‐minded thinking, future orientation, and avoidance of superstitious thinking), and a questionnaire assessing real‐world correlates in several domains (substance use, driving behavior, financial behavior, gambling behavior, electronic media use, and secure computing). Our heuristics and biases tasks and thinking disposition measures were modestly associated with several real‐world outcomes, including the domains of secure computing, financial behaviors, and the total scores. That is, better performance on the heuristics and biases measures was associated with fewer negative outcomes. We found that the associations were generally higher in males than in females. Heuristics and biases performance and thinking dispositions were unique predictors of real‐world outcomes after statistically controlling for educational attainment and sex differences. Copyright © 2016 John Wiley & Sons, Ltd.     

Tracing Attitude Expressions: An Eye‐Tracking Study

Attitudes represent object evaluations, comprising complex underlying cognitive and affective knowledge structures. When people are asked to judge an object, they can use their primary response (i.e., the immediate object‐evaluation linkage) or underlying affective and cognitive knowledge structures. In many situations, a primary response satisfices, but if not, more elaboration is required. Both processes are fundamentally different but may lead to the same attitude. For monitoring underlying processes during attitude expression, we developed an innovative eye‐tracking procedure using eye‐gaze on response scale options. This procedure was applied in three studies to identify the extent to which elaboration differs for attitude objects with weak or strong, univalent or mixed object evaluations (i.e., univalent, neutral and ambivalent). In Study 1, the overall judgment preceded processing of more specific affective and cognitive linkage evaluations. In Studies 2 and 3, the order was reversed, and affective and cognitive bases were assessed prior to overall attitude outcomes. For attitude objects with strong univalent or strong mixed object evaluations, we found similar outcomes on underlying processes. For weak object evaluations, cognition was found to be more predictive and easily accessible if an overall judgment was required first; affect for these objects was more predictive if people had to elaborate on affect and cognition first. We concluded that both affective and cognitive attitudes may require substantial elaboration, albeit in different situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Covariation assessment in rank order data

Two experiments were conducted to investigate how individuals assess covariation with rank order data. In both studies, subjects were given sets of rank order data, each set consisting of ten items ranked on two characteristics, and were asked to estimate the degree of relationship for each set. Contrary to previous research, subjects' estimates of covariation in this task were quite sensitive to actual levels of correlation in the data and remained unaffected by simple variations in the way rank order data were presented. More importantly, it appeared that this sensitivity to covariation was due likely to the use of a simple heuristic referred to here as the total discrepancy heuristic. These findings are discussed in terms of the availability of simple heuristics in rank-ordered versus other types of data and the consequences of using such heuristics in decision-making contexts.